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Characters on algebras of vector-valued continuous functions. (English) Zbl 1144.46046

Summary: Let \(A\) be a topological algebra with continuous multiplication, \(X\) a completely regular Hausdorff space and \(C(X,A)\) the algebra of all \(A\)-valued continuous functions on \(X\). We describe the characters on subalgebras of \(C(X,A)\) by means of those of \(A\) and evaluations at points of the Stone-Čech compactification of \(X\).

MSC:

46J10 Banach algebras of continuous functions, function algebras
46E40 Spaces of vector- and operator-valued functions
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References:

[1] P. Biström, S. Bjon and M. Lindström, Function algebras on which homomorphisms are point evaluations on sequences , Manuscripta Math. 73 (1991), 179-185. · Zbl 0764.46048
[2] S. Dierolf, K.H. Schröder and J. Wengenroth, Characters on certain function algebras , Funct. Approx. Comment Math. 26 (1999), 53-58. · Zbl 0932.46041
[3] W.E. Dietrich, The maximal ideal space for the topological algebra \(C(X, E)\) , Math. Ann. 183 (1969), 201-212. · Zbl 0169.17703
[4] H. El Adlouni and L. Oubbi, Caractères continus dans les algèbres à poids , Bull. Belg. Math. Soc. Simon Stevin 8 (2001), 567-575. · Zbl 1041.46029
[5] L. Gillman and M. Jerison, Rings of continuous functions , Van Nostrand, New York, 1960. · Zbl 0093.30001
[6] W. Govaerts, Homomorphisms of weighted algebras of continuous functions , Ann. Mat. Pura Appl. (4) 116 (1978), 151-158. · Zbl 0379.46014
[7] W.J. Hery, Maximal ideals in algebras of topological algebra valued functions , Pacific J. Math. 65 (1976), 365-373. · Zbl 0315.46048
[8] A. Mallios, Topological algebras, selected topics , North-Holland Math. Stud., vol. 124 -1986. · Zbl 0597.46046
[9] E.A. Michael, Locally multiplicatively convex topological algebras , Mem. Amer. Math. Soc. 11 , (1952). · Zbl 0047.35502
[10] L. Oubbi, Weighted algebras of continuous functions , Resources Math. 24 (1993), 298-307. · Zbl 0815.46040
[11] ——–, On different algebras contained in \(CV(X)\) , Bull. Belg. Math. Soc. Simon Stevin 6 (1999), 111-120. · Zbl 0923.46027
[12] J.B. Prolla, Topological algebras of vector-valued continuous functions , Adv. Math. Suppl. Stud. 7 (1981), 727-740. · Zbl 0469.46023
[13] J. Schmets, Espaces de fonctions continues , Lecture Notes in Math., vol. 519, Springer-Verlag, Berlin, New York, 1976. · Zbl 0334.46022
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